The Second Process

• The First Process

Now we are going to expand the Universe

Previously $\Omega ={\mathcal{P}}^1$ but now $\Omega ={\mathcal{P}}^1\cup {\mathcal{P}}^2$ we say $\Omega (t_1)={\mathcal{P}}^1(t_1)$ but $\Omega (t_2)=\stackrel{\text{this is not quite true}}{\overbrace{{\mathcal{P}}^2(t_2)\cup {\mathcal{P}}^2(t_1)}}$ saying that ${\mathcal{P}}^1(t)={\mathcal{P}}^1(t_1)={\mathcal{P}}^1$ so our original process has not changed, but

$${\mathcal{P}}^2(t_2)=\{{\Phi }_o^2(t_2),{\Phi }_i^2(t_2),{\tilde{\Phi }}^2(t_2),{\mathcal{F}}^2(t_2),{\mathcal{I}}^2(t_2)\}$$

Now ${\mathcal{P}}^2$ is a strictly controlled process, both in its input and its function, at $t_2$ at least , so we do not need to take measurement, for the nature of the output is solely controlled by the input, and there is a direct functional relationship between output of ${\mathcal{P}}^2$ and ${\mathcal{P}}^1$.

Let’s say ${\phi }_o^1(36)$ we begin passing into ${\mathcal{P}}^2$. ${\mathcal{I}}^2={\mathbb{N}}_0$ ${\Phi }_i^2(t_2)={\Phi }_o^1(t_2)$ and ${\phi }_i^2(i)={\phi }_o^1(36+i)$ ${\Phi }_o^2=\{{\Phi }_o^{2,1},{\Phi }_o^{2,2}\}$ ${\Phi }_o^{1,1}={\Phi }^{1,2}={\Phi }_1\cup {\Phi }_2\cup {\Phi }_3\cup {\mathcal{I}}^2$ Note that even though there are two ‘separate’ Objects emerging from ${\mathcal{P}}^2$, they are identified identically, so there is no extension to the Identity Space of ${\mathcal{P}}^2$.

Now ${\phi }_o^2=f({\phi }_i^2)$ Such that

$${\phi }_o^{2,1}(i)=\left[\begin{array}{lc}0.5& \text{if}{\phi }_{i{\Phi }_1}^2(i)\ge 0.5\\ {\phi }_{i{\Phi }_1}^2(i)& \text{otherwise}\end{array},{\phi }_{i{\Phi }_2}^2(i),{\phi }_{i{\Phi }_3}^2(i),i\right]$$ $${\phi }_o^{2,2}(i)=\{\begin{array}{ll}\varnothing & \text{if}{\phi }_{i{\Phi }_1}^2(i)<0.5\\ \left[{\phi }_{i{\Phi }_1}^2(i),{\phi }_{i{\Phi }_2}^2(i),{\phi }_{i{\Phi }_3}^2(i),i\right]& \text{otherwise}\end{array}$$